A STUDY ON DEBRIS FLOW OUTFLOW DISCHARGE AT A SERIES OF SABO … · 2014. 10. 26. · discharge at...

自然災害科学 J. JSNDS 33 特別号（2014） 43自然災害科学 J. JSNDS 33 特別号 43-52（2014）

A STUDY ON DEBRIS FLOW OUTFLOW DISCHARGE AT A SERIES OF SABO DAMS

Namgyun Kim＊・Hajime NAKAGAWA＊＊・Kenji KAWAIKE＊＊＊・Hao ZHANG＊＊＊＊

A STUDY ON DEBRIS FLOW OUTFLOW DISCHARGE AT A SERIES OF SABO DAMS

Namgyun KIM*, Hajime NAKAGAWA**, Kenji KAWAIKE*** and Hao ZHANG****

Abstract

Debris flows are very dangerous phenomena in mountainous areas. Sabo dams are commonly used to mitigate debris flows and they are effective countermeasures against debris flow disasters. However, human life and property remain at risk off debris flows. In order to develop measures to increase the effectiveness of a Sabo dam, its control function and design have been reported. Nevertheless, few studies have discussed the control functions of a series of Sabo dams. This paper estimates debris flow discharges at a Sabo dam site using overflow equations. A 1-D numerical simulation method of debris flows is presented. Numerical simulations of debris flow were conducted including overflow discharge at the dam point and laboratory experiments were performed to validate the simulation results. Comparisons between the numerical simulation results and laboratory experimental results show reasonable agreement. Application of the numerical model used here is recommended to calculate overflow discharge at Sabo dam sites and to evaluate the sediment capturing effects of Sabo dam arrangements.

Key words： debris flow, Sabo dam, overflow equation, deposition, numerical simulation

＊　　 Student Member of JSNDS, Doctoral Student, Department of Civil and Earth Resources Engineering, Kyoto University (Katsura Campus, Nishikyo-ku, Kyoto 615-8540, JAPAN)

＊＊　 Member of JSNDS, Dr. of Eng., Prof., DPRI, Kyoto University (Yoko-oji, Fushimi, Kyoto 612-8235, JAPAN)

＊＊＊　　 Member of JSNDS, Dr. of Eng., Assoc. Prof., DPRI, Kyoto University (Yoko-oji, Fushimi, Kyoto 612-8235, JAPAN)

＊＊＊＊　 Member of JSNDS, Dr. of Eng., Assist. Prof., DPRI, Kyoto University (Yoko-oji, Fushimi, Kyoto 612-8235, JAPAN)

43

A STUDY ON DEBRIS FLOW OUTFLOW DISCHARGE AT A SERIES OF SABO DAMS44

1. INTRODUCTIONMany types of sediment-related disasters occur

in mountainous areas (Fig. 1). Sediment-related

disasters are caused by localized torrential

downpours, earthquakes, volcanic eruption, and so

forth. These are natural phenomena. However, as

urbanization continues to expand in mountainous

areas, the risk of sediment-related disasters is

increasing. In particular, debris flows frequently

cause extensive damage to property and loss of life.

Debris flows are generally initiated from

upstream of a mountainous area when

unconsolidated material becomes saturated and

unstable or originate directly from landslides. They

can flow down several kilometers and damage the

residential areas at the foot of mountains. They

contain various particle sizes from fine material to

large boulders and these large boulders

accumulate at the front part of the flow. Thus

damage caused by debris flow can be severe. In

addition debris flows can cause morphological

changes, serious casualties and damage to

property. Figure 2 shows the number of debris

flow occurrences from 2000 to 2012 in Japan.

Countermeasures designed to reduce debris

flow disasters are classified into structural and non-

structural measures. Structural measures include

Sabo dams, guide levees and training channels,

while non-structural measures include warning

systems, proper land use in the areas and the

reinforcement of houses etc. Sabo dams are an

effective structural countermeasure to control

debris flow. They play an important role in the

management and development of a river basin.

Sabo dams can be distinguished into two types:

closed and open dams (Di Silvio., 1990; Armanini et

al., 1991). Closed-type Sabo dams intercept debris

flow to the downstream. In contrast, open-type

Sabo dams are constructed with suitable openings

in the body of the structure. Therefore part of the

sediment is allowed to pass through. These two

types of Sabo dams are constructed in series along

the channel.

The advance of science and technology has led to

more advantageous countermeasures for

mitigating debris flow damage. To increase the

effectiveness of Sabo dams, the control functions of

such dams have been reported. Such Sabo dam

functions have been described in many laboratory

experimental studies and numerical simulation

studies (Honda et al., 1997; Imran, J. et al., 2001).

Also, considerable theoretical and numerical works

have been performed on the size, shape and

structure of Sabo dams (Mizuyama et al., 1988; Johnson et al., 1989). These studies contribute to

technical standard guidelines on debris flows.

Thus, there are studies on methods of evaluating

the control function of a series of Sabo dams (Osti

et al., 2008). However, further studies are required

Fig.2 The number of debris flow occurrence in Japan

(Data source : MLIT, Japan)

Fig.1 Sediment-related disasters (Photo source :

DPWH, Japan)

自然災害科学 J. JSNDS 33 特別号（2014） 45

to develop general guidelines on a series of Sabo

dams. Few studies have reported about control

functions of a series of Sabo dams.

This paper describes a methodological approach

for estimating debris flow discharge at a series of

Sabo dams, and proposes equations for evaluating

the effectiveness of a series of closed-type Sabo

dams. A 1-D numerical model of debris flow is

presented. Numerical simulations were conducted

including debris flow overflow at the dam point and

analyzed with boundary conditions. To verify the

suggested numerical model , laborator y

experiments were performed.

The numerical model is used to study the effect

of Sabo dam arrangement. Through the proposed

calculation method of overflow discharge at the

dam point, determination of optimal distance

between Sabo dams is expected.

2. NUMERICAL MODEL2.1 Governing Equations

(1) Transport and bed surface elevation equations

Debris flows are a fluid mixture that consists of

granular materials and water. The equations used

are the depth averaged one-dimensional

momentum and continuity equations. The

equations for the mass conservation of sediment-

water mixture and mass conservation of sediment

are as follows.

Momentum equation of sediment and water flow

mixture:

(1)

Continuity equation of flow mixture:

(2)

Continuity equation of sediment particles:

(3)

where, M (= uh) is the x components of the flow

flux, x is the flow direction coordinate, t is time, β is

the momentum correction factor equal to 1.25 for a

stony debris flow (Takahashi et al., 1992), u is the

components of mean velocity, g is the acceleration

of gravity, h is flow depth, θb is the bed slope, τ

b is

components of the resistance to flow, ρT is mixture

density (ρT=σC+(1-C)ρ), σ is density of the sediment

particle, ρ is density of the water, i is erosion (>0) or

deposition (≤0) velocity, C is the sediment

concentration in the flow, C* is maximum sediment

concentration in the bed.

The equation of bed variation due to erosion or

deposition is described as follows:

(4)

where, zb is erosion or deposition thickness of the

bed measured from the original bed surface

elevation. In the fixed bed, zb equals 0. Actually, the

sediment in the fixed bed should be contained in

the flow parts when erosion occurs. However there

is no sediment in the fixed bed.

(2) Erosion and deposition velocity equations

The erosion and deposition i are source terms.

The velocity equations that have been given by

Takahashi et al. (1992) are described as follows:

Erosion velocity, if C < C∞;

(5)

Deposition velocity, if C ≥ C∞;

(6)

where, δ is erosion coefficient, δ' is deposition


coefficient, dm is mean diameter of sediment, and

C∞ is the equilibrium sediment concentration

described as follows (Nakagawa et al., 2003).

If tanθw > 0.138, a stony type debris flow occurs,

and

(7)

If 0.03< tanθw

≤ 0.138, an immature type of debris

flow occurs, and

(8)

If tanθw ≤ 0.03, a turbulent water flow with bed load

transport occurs, and

(9)

(10)

(11)

(12)

where, θw is water surface gradient, ρ

m is density

of the interstitial muddy fluid, ϕ is internal friction

angle of the sediment τ*c

is the non-dimensional

critical shear stress and τ* is the non-dimensional

shear stress.

(3) Bottom shear stress equations

The resistance terms are given by the following

equations for a stony debris flow:

(13)

An immature debris flow occurs when C is less

than 0.4C* and the bottom shear stress is described

as follows:

(14)

In the case of turbulent flow, the Manning’s

equation is used to determine the bottom shear

stress. When C is less than 0.02,

(15)

where, n is the Manning resistance coefficient.

2.2 Conditions of Sabo DamThe closed-type Sabo dam is set at the grid line

where discharge is calculated (Fig. 3). The grid

size is 5 cm. The flow surface gradient, θw, and bed

gradient, θb, are calculated at the center of the cell.

The flow surface gradient θw and bed gradient θ

b are

calculated by the average of each value of θw, i+1,

θb, i+1 and θ

w, i-1, θb, i-1. However, if there is a Sabo dam,

the calculation method is changed as follows:

Gradient at the dam point (zi < z

dam);

(16)

(17)

Gradient at the dam point (zi ≥ z

dam);

(18)

Fig.3 Definition of the variables


(19)

2.3 Overflow EquationsSabo dams involve obstructing the path of flow.

This is a vertical obstruction over which the debris

must flow such as a weir. At that time, outflow

discharge at the dam point can be calculated using

certain equations. To calculate debris flow

discharge at the dam point, the overflow equation

and free overfall equation are applied.

Overflow equation (Complete flow):

(20)

Overflow equation (Incomplete flow):

(21)

Free overfall equation:

(22)

where, M0 is debris flow discharge per unit width

at the dam point, and c is the overflow coefficient.

As the overflow equation and free overfall equation

are adjusted at the dam point, flow conditions are

changed by the bed elevation (Table 1).

3. LABORATORY EXPERIMENTS

Figure 4 shows the experimental flume setup.

The laboratory experiments were conducted using

a rectangular flume, which is 6.5m long, 13 cm

high, 10 cm wide and has an incline of 18°. The

flume is divided into two parts by an 8cm high sand

stopper that is installed 1.5m from the upstream

end of the flume. The upstream part is filled with a

movable bed that consists of silica sand and gravel

Table 1 Flow conditions at Sabo dam

Fig.4 Experimental flume setup


mixtures. The movable bed was set 20cm upstream

from the upstream end of the flume, length 150 cm,

8 cm high, and 10 cm wide. Sediment materials

with mean diameter dm=2.86mm, maximum

diameter dmax

=15mm and density σ=2.65g/cm3,

internal friction angle of a sediment tanϕ=0.7 were

used. The particle size distribution of the movable

bed is shown in Figure 5.To generate the debris flow, the movable bed is

saturated by seepage flow. After fully saturating the

movable bed, the debris flow is generated through

supplying clear water. The debris flow developed in

the experiments is fully stony type debris flow and

larger particles are accumulated at the forefront of

the debris flow. This debris flow, overtopping the

sand stopper, reaches the downstream part of the

flume. After overtopping the two Sabo dams, debris

flows are captured by the sampler.

The experimental conditions are shown in Table 2. Two closed-type Sabo dams 6 cm high, 10 cm

wide and 1 cm thick were used for the

experiments. The lower Sabo dam was set 30 cm

upstream from the downstream end of the flume

the upper Sabo dam was set 30 cm, 55 cm, 80 cm

upstream from the lower Sabo dam.

Two runs were conducted under the same

experimental conditions in order to obtain reliable

data. Debris flow discharge and sediment

concentration at each dam point were measured

using sampler. Debris flow deposition upstream of

the Sabo dam was measured by video camera and

the images were analyzed over time.

4. RESULTS AND DISCUSSIONThe numerical simulations were conducted to

calculate debris flow discharge at the dam point

and experiments were also performed to validate

the numerical model.

Figure 6 shows the simulated results and

experimental results of debris flow discharge and

sediment concentration. In this graph, time 0 means the start time to supply clear water. The

start time of blue line means the time the debris

flow reached the upper Sabo dam. Table 3 shows

the time the debris flows reached each position.

In Case A, the overflow time of debris flow at the

lower Sabo dam is earlier than in Case B and Case

C. The distance between two Sabo dams is not

sufficient capture debris flow. Sufficient distance

Fig. 5 Particle size distribution of sediment materials

Table 2 Experimental conditions

Table 3 Debris flow time (unit : sec)


between two Sabo dams means that the length

between two Sabo dams is longer than the

deposition length upstream of one Sabo dam. This

deposition starting from the Sabo dam to the

deposition height is equal to 0.Table 4 shows the debris flow peak discharge.

In the experimental results, debris flow discharge

is calculated at the downstream end of the flume

Table 4 Debris flow peak discharge (unit : cm3/s)

Fig .6 Debris flow discharge (a) and sediment concentration (b)


under the no Sabo dam case. Simulated results of

debris flow discharge are consistent with the

experimental results. Through the series of Sabo

dams, the total discharge of debris flow and peak

discharge is decreased.

The total average peak discharge rate is 48.4% in

the experimental results and 48.1% in the

simulation results. However, the longer the

distance between two Sabo dams, the higher the

rate of total discharge decrease. The situation is

different in the lower Sabo dam. The longer the

distance between two Sabo dams, the easier it is to

form a fully developed debris flow.

The average decrease rate of the upper Sabo

dam is 29.8% in the experimental results and 31.9%

in the simulation results. However, the average

decrease rate of the lower Sabo dam is 18.6% in the

experimental results and 16.2% in the simulation

results. The efficiency of the decrease rate of

debris flow peak discharge at the lower Sabo dam

is less than the upper Sabo dam. The reason for

this is the sediment concentration. In the Figure 6(b), as debris flows pass the Sabo dam, sediment

concentration decreased. First, the sediment

concentration is consistent at around 35%. As the

debris flows passed the upper Sabo dam, sediment

concentration decreased to around 30% and when

passing the lower Sabo dam, sediment

concentration fur ther decreased. However,

overflowed debris flow at the lower Sabo dam does

not have a consistent sediment concentration. The

initial sediment concentration is lower than 5%.

This means that debris flow that is not fully

developed reaches the lower Sabo dam. As debris

flows overflow the Sabo dam, sediment is captured

by the Sabo dam. Therefore, the forefront of the

debris flow has a low sediment concentration.

Figure 7 shows the debris flow deposition

upstream of the Sabo dam. In this graph, time 0 means the start time of debris flow being captured

by the Sabo dam. Some discrepancies are found in

the shape of the deposition between the simulated

results and experimental results. The height of

deposition in the experimental results is higher

than that in the simulation results. The simulation

results are underestimated. Therefore, a more

feasible coef ficient of erosion velocity and

coefficient of deposition velocity are required.

Through adjusting the discharge coefficient and

erosion, deposition coefficient, the debris flow

deposition pattern could be further improved.

In this study the debris flow overflow discharge

at a series of Sabo dams was evaluated. The

suggested simulation method for calculating debris

flow discharge results in good agreement with the

experimental results.

5. CONCLUSIONSThe numerical model was developed to simulate

the debris flow discharge at the dam point.

Laboratory experiments were conducted and good

results of debris flow discharge as well as sediment

concentration were obtained. Debris flow

deposition will be further improved through

adjustment of the coefficient.

Through considering the combination of Sabo

dams, elucidation of technical criteria on the

distance between Sabo dam is expected.

ACKNOWLEDGMENTThis research was supported by the JSPS AA

Science Platform Program (Coordinator: H.

Nakagawa) and support of the Wakate fund

program by the Kyoto University Global COE

Program (GCOE-ARS).

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Fig. 7 Debris flow deposition upstream of Sabo dam


2: Erosion control works. Lecture Notes, IHE,

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Honda N., Egashira S., 1997. Prediction of debris flow

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A STUDY ON DEBRIS FLOW OUTFLOW DISCHARGE AT A SERIES OF SABO … · 2014. 10. 26. · discharge at...

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